M.Mnatsakanova, G.Morchio, F.Strocchi, Yu.Vernov Irreducible representations of the Heisenberg algebra in Krein spaces (49K, TeX) ABSTRACT. The representations of the Heisenberg algebra in Krein spaces, more generally in weakly complete inner product spaces, are classified under general regularity and irreducibility conditions. Besides the Fock representation, two other types appear, one with negative, the other with two sided discrete spectrum of the number operator.